the commercial egg operations would be feeding it.
Not really. They control when their specially bred hybrids start to lay mainly by manipulating lights. They tailor what they feed them to match when they start them laying by manipulating the lights. They don't want them to start laying too early.
Why, you ask, do they not want them laying really early? With their breeding they could have most of them popping out eggs as early as 16 weeks. Money, of course. A small part is that the first pullet eggs are pretty small, they don't get as good a price for small pullet eggs as they will when the eggs get a little larger, so they delay the start of egg laying a few weeks for that. It's not at all unusual for a pullet's first eggs to be strange: soft shelled, no shell, a really thick shell, double yolked, no yolk, only yolk, or something else that is weird. Not only are most of these eggs not marketable they can mess up the egg gathering and handling system. But more important is the pullets' health. If they start laying really young they are more prone to prolapse, internal laying, or egg binding. On the commercial scale this can be significant. Even if these don't kill the pullet outright, they can mess them up for future egg laying. Anything that disrupts the normal system needs special handling, which costs time. They find it more beneficial to allow the pullet's internal egg making factory to mature a bit before they start popping out eggs that are more marketable and less threatening to the pullets health.
From reading about when they change diets to get them ready to lay eggs, I think most start producing eggs around 22 to 23 weeks of age.
Does this question make sense at all? If it does, is it an accurate way to factor the average for egg laying age?
The question makes perfect sense. In some was it's not a horrible way to predict the average age of egg laying. After all the pullets inherit those genes from both mother and father. As others mentioned there are several other factors that will affect when they actually start to lay.
You mentioned a key word, average. Each chicken is an individual and pretty much does its own thing. Some will start laying very young, others of the same breed or even same parents can wait a long time. You have to have enough chickens for averages to mean something. Very few of us do.
There is another flaw if you are going by breed. From what I read on this forum some people seem to think that all chickens of the same breed are identical. Not even close to true. If the person that selects which chickens get to breed uses how early they start egg laying as a criteria they can have a flock that pretty consistently beats the breed average in just a few generations. If they do not use that as a criteria they may wind up with a flock of the same breed that is consistently slower than breed average. If you know when the mother started and and when the hen and rooster's mothers and grandmothers started you may get an idea of what each is contributing genetically, which may help you with averages. It still doesn't indicate what any specific pullet will do.
I understand the frustration of waiting for them to start. I once waited 9 months for a group of three pullets to lay their first egg, my first blue eggs. By the flock they came from they should have started around 5 to 6 months. I have no idea what happened, neither did the breeder I got them from. Their daughters surprised me by starting laying around 5 to 6 months. as Aart said, they lay when they lay.